I work for a group at our educational institution that licenses its software with a license that is verbatim the BSD 3-clause license with one sentence added under the copyright year/holder line. The top of the license reads thus:

1 Answer
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This should not make any difference. It just reaffirms something that is true anyway. Similarly, the phrase “all rights reserved” next to a copyright notice is completely superfluous nowadays.

But since it (probably) makes no difference, yet leads to potential confusion, you might want to inquire why your institution is using this. Was there specific guidance from your legal department? Or did someone add that sentence, and everyone copied it without considering whether it is necessary? I think it would be clearer if this line was deleted.